在過去文獻中很少討論在廣義線性模式中同時有測量誤差和隨機效用，主要是因為將隨機效用積分後的分配已不是廣義線性模式，使得傳統上的條件分數法或是校正分數法難以應用。本文主要探討邏輯斯迴歸在有測量誤差和隨機效用時的模型中，使用部分條件分數估計方法，並與 Naive 及迴歸校正法兩者作比較。

There are not many literatures discuss the statistical inference when the measurement error and random effect exist in the generalized linear model. The main reason is that the distribution after integrating the random effect is no  longer a generalized linear model, hence the conventional conditional score or corrected score are difficult in application. This paper discussed the estimation method when measurement error and random effect coexist in the logistic regression model, the estimation was done by a partially conditional score. We compare the efficient of the methods of Naive and regression calibration with the proposed method by simulation studies.

目錄
第1 章緒論 1
第2 章自變數含有測量誤差之邏輯斯隨機效應模型 4
2.1 符號的定義 4
2.2 模型 5
第3 章估計方法 7
3.1 Naive 估計法 7
3.2 迴歸校正法(Regression Calibration ; RC) 8
3.3 部分條件分數法(Partially Conditional Score) 8
第4 章模擬研究 12
4.1 模擬設定 12
4.2 模擬結果 13
第5 章結論 14
附錄 15
參考文獻 24

參考文獻
Carroll, R. J., Rupper, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement error in nonlinear models. Chapman and Hall, New York.
Chan, Jennifer S.K. and Kuk, Anthony Y.C. (1997). Maximum Likelihood Estimation for Probit-Linear Mixed Models with Correlated Random Effects. Biometrics, V. 53, No. 1, 86-97.
Nakamura, T. (1990). Corrected Score Function for Errors-in-Variables Models: Methodology and Application to Generalized Linear Models. Biometrika, V. 77, No. 1, 127-137.
Schall, R. (1991). Estimation in Generalized Linear Models with Random Effects. Biometrika, V. 78, No. 4, 719-727.
Stefanski, L. A. and Carroll, R. J. (1987). Conditional Scores and Optimal Scores for Generalized Linear Measurement  Error Models. Biometrika, V. 74, No. 4, 703-716.
Stefanski, L. A., Novick, S. J. and Devanarayan, V. (2005) Estimating a nonlinear function of a normal mean. Biometrika, V. 92, No. 3, 732-736.
Wang, N., Lin, X., Gutierrez, R. G. and Carroll, R. J. (1998). Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models. Journal of the American Statistical Association, V. 93, No. 441, 249-261.
Zhong, X., Fung, W. and Wei, B. (2002). Estimation in linear models with random effects and errors-in-variables. Ann. Inst. Statist. Math. V. 54, No. 3, 595-606.
余佳倫(2012). On the estimation methods for the generalized linear mixed effect model with measurement error. 中華民國淡江大學碩士論文.
張瑞君(2008). A consistent estimation in log-linear mixed measurement error models. 中華民國淡江大學碩士論文.
魏鈺方(2005). Estimating methods in linear and probit models with measurement errors and without extra information. 中華民國淡江大學碩士論文.